1. Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2

2. Recursive Formula: An ordered list of numbers defined by a starting value (number) and a rule to find the general term. A(1) = A(n) =General term or n th term first term A(n-1)=Previous term Given the following recursive formula, find the first 4 terms. A(1) =20 A(n) = A(n-1) + 6 20,26,32,38 1 st term 2 nd term 3 rd term 4 th term A(1) = 20 A(2) = A(2-1) + 6 A(1) + 6 20 + 6 A(2) = 26 A(n) =A(n-1) + 6 A(3) =A(3-1) + 6 A(2) + 6A(3) = 26 + 6A(3) = 32 A(n) =A(n-1) + 6 review

3. Explicit Formula: a function rule that relates each term of the sequence to the term number. A(n) = A(1) + (n-1)d nth term 1 st term Term number Common difference Write an explicit formula given the following sequence and then find the 5 th term. 20, 26, 32, … Find it without the formula: 20, 26, 32, ___, ____,38 44 A(n) = A(1) + (n -1)d Now, write and use the formula to find the 5 th term: A(1) = 20 d = 6 n = 5 A( ) = + ( -1) 20 5 6 5 A( 5 ) = 20 + (4)6 A( 5 ) = 44

4. Write an explicit formula for each recursive formula. A(1) = 19 A(n) = A(n-1) + 12 A(n) = A(1) + (n-1)d A(n) = + (n-1) 19 12 A(1) = 5 A(n) = A(n-1) - 3 A(n) = A(1) + (n-1)d A(n) = + (n-1) 5 (-3) Find the 2 nd, and 10 th terms of the sequence on the left.. A( ) = + ( -1) 2 19212 A(2) = 19 + (1)12 A(2) = 19 + 12 A(2) = 31 A( ) = + ( - 1) 1019 10 12 A( 10) = 19 + (9) 12 A( 10) = 19 + 108 A( 10) = 127

5. Write a recursive formula for each explicit formula. A(n) = 32 + (n -1)12 A(1) = A(n) = A(n-1) 32 + 12 A(n) = 10 + (n -1)(- 4) A(1) = A(n) = A(n-1) 10 A(n) = 10 + (n -1)(- 4) - 4 Assignment: Page 279: 38-44 evens, 46-53, 66-67, 76,77, 80